2.5.4 Commands and Functions returning LIST |
apply | apply homomorphism |
ApproxSolve | Approximate real solutions for polynomial system |
ArrBettiNumbers | Betti numbers of an arrangement of hyperplanes |
ArrBoolean | boolean arrangement |
ArrBraid | braid arrangement |
ArrCatalanA | Catalan arrangement of type A |
ArrCatalanB | Catalan arrangement of type B |
ArrCatalanD | Catalan arrangement of type D |
ArrCone | cone of an arrangement of hyperplanes |
ArrDeletion | deletes a hyperplane from a list of hyperplanes |
ArrExponents | exponents of a free arrangement of hyperplanes |
ArrFlats | list of flats of an arrangement of hyperplanes |
ArrGraphical | graphical arrangement |
ArrLattice | lattice of an arrangement of hyperplanes |
ArrRestriction | arrangement of hyperplanes A restricted to a hyperplane |
ArrShiA | Shi arrangement of type A |
ArrShiB | Shi arrangement of type B |
ArrShiCatalanA | Shi-Catalan arrangement of type A with multiplicities |
ArrShiCatalanB | Shi-Catalan arrangement of type B with given multiplicities |
ArrShiCatalanD | Shi-Catalan arrangement of type D with given multiplicities |
ArrShiD | Shi arrangement of type D |
ArrSignedGraphical | signed graphical arrangement |
ArrToMultiArr | multiarrangement from an arrangement and a list of multiplicities |
ArrTypeB | reflection arrangement of type B |
ArrTypeD | reflection arrangement of type D |
ascii | convert between characters and ascii code |
BBasis5 | Border Basis of zero dimensional ideal |
BettiNumbers | (Multi-)graded Betti numbers |
BinomialRepr, BinomialReprShift | binomial representation of integers |
CartesianProduct, CartesianProductList | Cartesian product of lists |
CFApproximants | continued fraction approximants |
coefficients | list of coefficients of a polynomial |
CoefficientsWRT | list of coeffs and PPs of a poly wrt indet or list of indets |
CoeffListWRT | list of coefficients of a polynomial wrt an indet |
CoeffListWRTSupport | list of coefficients of a polynomial wrt a power-product basis |
compts | list of components of a ModuleElem |
concat | concatenate lists |
ConcatLists | concatenate a list of lists |
ContFrac | continued fraction quotients |
CoprimeFactorBasis | determine coprime factor base for a set of integers or ring elements |
covers | a poset description from the list of the strict relations |
CurrentTypes | lists all data types |
diff | returns the difference between two lists |
distrib | the distribution of objects in a list |
eigenfactors | eigenfactors of a matrix |
eigenvectors | eigenvalues and eigenvectors of a matrix |
EquiIsoDec | equidimensional isoradical decomposition |
exponents | the list of exponents of the leading term of a polynomial |
ExternalLibs | Linked external libraries |
FGLM5 | perform a FGLM Groebner Basis conversion |
fields | list the fields of a record |
flatten | flatten a list |
FrbAlexanderDual | Alexander Dual of monomial ideals |
FrbAssociatedPrimes | Associated primes of monomial ideals |
FrbIrreducibleDecomposition | Irreducible decomposition of monomial ideals |
FrbMaximalStandardMonomials | Maximal standard monomials of monomial ideals |
FrbPrimaryDecomposition | Primary decomposition of monomial ideals |
GBasis | calculate a Groebner basis |
GBasisByHomog | calculate a Groebner basis by homogenization |
GBasisTimeout | compute a Groebner basis with a timeout |
GenericPoints | random projective points |
GenRepr | representation in terms of generators |
gens | list of generators of an ideal |
GensJacobian | set of generators of the Jacobian ideal of a polynomial |
GetCol | convert a column of a matrix into a list |
GetCols | convert a matrix into a list of lists |
GetRow | convert a row of a matrix into a list |
GetRows | convert a matrix into a list of lists |
GraverBasis | Graver basis |
GroebnerFanIdeals | all reduced Groebner bases of an ideal |
GroebnerFanReducedGBases | Groebner fan reduced GBases |
HilbertBasisKer | Hilbert basis for a monoid |
homog | homogenize wrt an indeterminate |
HVector | the h-vector of a module or quotient object |
in | list element selector in list constructor |
indets | list of indeterminates in a PolyRing |
IndetSubscripts | the indices in the name of an indeterminate |
interreduced | interreduce a list of polynomials |
intersection | intersect lists, ideals, or modules |
IntersectionList | intersect lists, ideals, or modules |
InverseSystem | Inverse system of an ideal of derivations |
JanetBasis | the Janet basis of an ideal |
LinKerBasis | find the kernel of a matrix |
MakeSet | remove duplicates from a list |
MaxChains | computes all the maximal chains from the relations of the poset |
MinGens | list of minimal generators |
minors | list of minor determinants of a matrix |
MinSubsetOfGens | list of minimal generators |
moebius | Moebius function of a poset |
monomials | the list of monomials of a polynomial |
MultiArrExponents | exponents of a free multiarrangement of hyperplanes |
MultiArrRestrictionZiegler | Ziegler multirestriction of the arrangement of hyperplanes wrt a hyperplane |
MultiArrToArr | underling arrangement from a multiarrangement |
NewList | create a new list |
NmzDiagInvariants | ring of invariants of a diagonalizable group action |
NmzEhrhartRing | Ehrhart ring |
NmzFiniteDiagInvariants | ring of invariants of a finite group action |
NmzIntClosureMonIdeal | integral closure of a monomial ideal |
NmzIntClosureToricRing | integral closure of a toric ring |
NmzIntersectionValRings | intersection of ring of valuations |
NmzNormalToricRing | normalization of a toric ring |
NmzTorusInvariants | ring of invariants of torus action |
NonZero | remove zeroes from a list |
operators, shortcuts | Special characters equivalent to commands |
packages | list of loaded packages |
partitions | partitions of an integer |
permutations | returns all permutations of the entries of a list |
PosetDual | dual of a poset from the relations of the poset |
PosetJoin | join between two elements of a poset from the relations of the poset |
PosetMeet | meet between two elements of a poset from the relations of the poset |
PrimaryDecomposition | primary decomposition of an ideal |
PrimaryDecompositionGTZ0 | primary decomposition of a 0-dimensional ideal |
QuotientBasis | vector space basis for zero-dimensional quotient rings |
QuotientBasisSorted | vector space basis for zero-dimensional quotient rings |
QZP | change field for polynomials and ideals |
RandomPermutation | random permutation (of indices) |
RandomSubset | random subset |
RandomSubsetIndices | indices for random subset |
RandomTuple | random tuple |
RandomTupleIndices | indices for random tuples |
RationalAffinePoints | Affine rational solutions |
RationalProjectivePoints | Projective rational solutions |
RationalSolve | Rational solutions for polynomial system |
RealRoots | real roots of a univariate polynomial |
RealRootsApprox | approximations to the real roots of a univariate poly |
ReducedGBasis | reduced Groebner basis |
res | free resolution |
reverse, reversed | reverse a list |
RingElems | convert an expression into a RINGELEM |
RingsOf | list of the rings of an object |
SeparatorsOfPoints | separators for affine points |
SeparatorsOfProjectivePoints | separators for projective points |
shape | extended list of types involved in an expression |
sorted | sort a list |
SortedBy | sort a list |
starting | list functions starting with a given string |
StdBasis | Standard basis |
SturmSeq | Sturm sequence of a univariate polynomial |
subsets | returns all sublists of a list |
support | the list of terms of a polynomial or moduleelem |
SymbolRange | range of symbols for the indeterminates of a PolyRing |
SymmetricPolys | list of symmetric polynomials |
tail | remove the first element of a list |
TopLevelFunctions | returns the functions available at top-level |
tuples | N-tuples |
TVecFromHF | Type vector from Hilbert Function |
UniversalGBasis | universal Groebner basis of the input ideal |
wdeg | multi-degree of a polynomial |
WithoutNth | removes the N-th component from a list |
ZPQ | change field for polynomials and ideals |